Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

Abstract

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ei, with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors |ei⋅ˆω| are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e1, in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e1 and that the strongly swirling worms are kinematically significant to this process.